Chroma key, translate forground, retrieve video from sequence editor
Part 1: The Mask node is (usually) see below rendered at Project dimensions. If your image is not the same size as the Blender project then the mask will not fit. Even if you have drawn it to match in the MCE or UV Image editor.

In this image notice that the mask was drawn to fit around the cube but the rendered version is to small.



Use Scale node with Render Size selected, and choose Fit if the aspect ratio of the image is different to the render dimensions.



Notice that the Mask node can be in Scene Size...



*...or you could make it a predetermined size (to match your source media)



To move the keyed image around, first use the Set Alpha node then the Transform node. You can choose to filter these transformations with Bicubic (better quality).



Also you should use an Alpha Over node to combine a keyed image, instead of a Mix node.

Answering Part 2: You cannot send the output of the VSE to the compositor, sorry. You would have to render it first or copy the values (from the VSE Strip) for frame start and length to a Image/movie node. There is a script that will do this for you. Related Can I add the output of the VSE as input to the node diagram?